The long term goal of this work is to derive and test new, improved approaches to coincidnc timing especially for the case of scinitillation signals obtained from positron annihiliation events. Improved timing measurement will reduce the random coincidence rate with slower scintillators such as BGO. This in turn will permit design of PET instruments capable of more accurate imaging of larger doses of short half-life agents such as 15O or 17F. In the case of fast scintillators such as BaF2, improved timing reduces the uncertainty in the location of the positron annihilation along the ray. This is equivalent to increasing the sensitivity of a Time-of-Flight positron tomography since the signal-to-noise ratio in the reconstructed image is improved for a given number of detected events. Estimation theory based o a detailed model of the detection system will be used to derive efficient, robust, and accurate estimates of the photon arrival time. These etimates will be theoretically and experimentally compared to conventional timing methods which use leading edge and constant fraction triggers. Finally, experimental methods for implementing these estimators for a large multi-channel system will be devised.